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In this article we prove a reducibility result for the linear Schrödinger equation on the sphere $\mathbb{S}^n$ with quasi-periodic in time perturbation. Our result includes the case of unbounded perturbation… Click to show full abstract
In this article we prove a reducibility result for the linear Schrödinger equation on the sphere $\mathbb{S}^n$ with quasi-periodic in time perturbation. Our result includes the case of unbounded perturbation that we assume to be of order strictly less than $1/2$ and satisfying some parity condition. As far as we know, this is one of the few reducibility results for an equation in more than one dimension with unbounded perturbations. Letus note that, surprisingly, our result does not require the use of the pseudo-differential calculus although the perturbation is unbounded.
Journal Title: International Mathematics Research Notices
Year Published: 2020
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